Using operations of sum/subtraction with fractions, it is found that he must gain [tex]\frac{1}{5}[/tex] of miles of elevation on the fourth day.
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- On the first day, his net elevation was of [tex]-\frac{1}{4}[/tex]
- On the second day, his net elevation was of [tex]\frac{1}{2}[/tex]
- On the third day, his net elevation was of [tex]-\frac{1}{5}[/tex]
- On the fourth day, his net elevation was of x.
- We want to total to be of [tex]\frac{1}{4}[/tex].
- Thus, we have to solve the sum of the four days equal to [tex]\frac{1}{4}[/tex] for x.
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[tex]-\frac{1}{4} + \frac{1}{2} - \frac{1}{5} + x = \frac{1}{4}[/tex]
[tex]\frac{-5 + 10 - 4 + 20x}{20} = \frac{1}{4}[/tex]
[tex]\frac{1 + 20x}{20} = \frac{1}{4}[/tex]
[tex]1 + 20x = 5[/tex]
[tex]20x = 4[/tex]
[tex]x = \frac{4}{20} = \frac{1}{5}[/tex]
He must gain [tex]\frac{1}{5}[/tex] of miles of elevation on the fourth day.
A similar problem is given at https://brainly.com/question/16521826
